Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
Eduardo Casas, Fredi Tröltzsch (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented. ...